Question

Assertion (A): A standing wave is produced in a string clamped at one end and free at the other end. The length of string is odd multiples of $\frac{\lambda }{4}$.

Reason (R): Distance between successive node and antinode is $\frac{\lambda }{4}$.

• A. Both assertion and reason are true and reason is the correct explanation of assertion
• B. Both assertion and reason are true but reason is not the correct explanation of assertion.
• C. Assertion is true but reason is false
• D. Both assertion and reason are false

Answer 1

The correct option is B Both assertion and reason are true but reason is not the correct explanation of assertion.

At the clamped end always a node is formed and at the tree end , an antinode is formed.
distance between a node and antinode is $\frac{\lambda }{4}$
$\therefore$ so total length is $n\left(\frac{\lambda }{2}\right)+\frac{\lambda }{4}=(2n+1)\frac{\lambda }{4}$